We study constructive interference based block-level precoding (CI-BLP) in the downlink of multi-user multiple-input single-output (MU-MISO) systems. Specifically, our aim is to extend the analysis on CI-BLP to the case when the number of symbol slots in a given transmission block is smaller than the number of users. To this end, we mathematically prove the feasibility of using the pseudo-inverse to obtain a closed-form structure of the optimal CI-BLP precoding matrix. Similar to the case when the number of symbol slots in a given transmission block is not smaller than the number of users, we show that a quadratic programming (QP) optimization on simplex can be constructed. We also design a low-complexity algorithm based on the alternating direction method of multipliers (ADMM) framework, which can achieve a flexible trade-off between communication performance and execution time by modifying the maximum number of iterations. We further analyze the convergence and complexity of the proposed algorithm. Numerical results validate our analysis and the optimality of the QP optimization, and further show that the proposed ADMM algorithm can provide satisfactory results in dozens of iterations, which motivates the use of CI-BLP in practical wireless systems.

This paper designs a parallel solution framework for constructive interference based symbol-level precoding (CI-SLP) in the downlink of a multi-user multiple-input single-output (MU-MISO) system. Most existing works on SLP have considered the sum-power constraint, while in practical systems each transmit antenna is equipped with its dedicated power amplifier. Therefore, it is more realistic to design SLP approaches that incorporate the per-antenna power constraint (PAPC). In this paper, we focus on two specific PAPC-based problems: the constructive interference per-antenna power constraint signal to interference plus noise ratio (SINR) balancing (CI-PASB) problem and the constructive interference per-antenna peak power minimization (CI-PAPM) problem. Similar to sum-power constraint, for the CI-PASB problem, we demonstrate that it is separable, allowing the existing parallel proximal Jacobian alternating direction method of multipliers (PJ-ADMM) algorithm to be directly used. As for the CI-PAPM problem, although it is unseparable, we can leverage the established duality to obtain its solution based on the solution of the corresponding CI-PASB problem. Numerical results verify our proposed parallel methods and show that they are more efficient than the existing centralized schemes, which showcases the advantages of parallel computing and promotes the implementation of CI precoding under practical PAPC scenarios.

We study constructive interference based block-level beamforming (CI-BLB) in the downlink of multi-user multiple-input single-output (MU-MISO) systems. CI-BLB achieves im-proved performance over the traditional CI-based symbol-level beamforming (CI-SLB) method, because of its more intelligent power allocation scheme over the considered block of symbol slots. In this paper, we design a low-complexity algorithm based on the alternating direction method of multipliers (ADMM) framework, which can efficiently solve QP problems. We analyze the convergence and complexity of the proposed algorithm. Nu-merical results validate the optimality of the proposed algorithm, and further show that the proposed algorithm offers a flexible performance-complexity tradeoff by limiting the maximum num-ber of iterations, which motivates the use of CI - BLB in practical wireless systems.

This paper addresses the constructive interference (CI) precoding problem under per-antenna power constraint (PAPC) in the downlink of multi-user multiple-input single-output (MU-MISO) systems. In this setup, we extend the phase rotation metric and symbol scaling metric of CI precoding under sum power constraint (SPC) to the scenario of PAPC. Against SPC, the scenario of PAPC represents a practical constraint acknowledging that each antenna would have its dedicated power amplifier. Nevertheless, the optimization problem of CI-PAPC precoding becomes more challenging than that under SPC. By analyzing the KKT conditions and leveraging the generalized matrix inverse theory, we obtain a closed-form structure of the CI-PAPC precoder as a function of introduced variables, which facilitates a low-complexity solver. Since the power constraint of each antenna is not always active under PAPC, existing iterative schemes under CI-SPC are no longer applicable. Therefore, the primal-dual interior point method (IPM) is employed to solve the simplified problem with reduced complexity and fast convergence. Simulation results verify our mathematical derivations and demonstrate that our proposed method can reduce the complexity of solving CI-PAPC problem while preserving the error-rate performance, which promotes the practical implementation of CI precoding in real PAPC scenarios.